A fundamental component of many devices that receive or otherwise process transmitted waveforms of a certain, known character is the matched filter. Such devices include communication receivers and radar-based automatic target recognition systems, as well as a host of other communications and signal processing devices. The wide applicability of the matched filter with such devices stems from the matched filter's relative simplicity and its optimal functioning within the context of an environment that can be modeled as a linear Gaussian system.
Few if any other systems characterized as linear perform better than those using the matched filter if the template of the transmitted signal is known. More particularly, a signal template, sk, existing during the time interval [0, T] and corrupted by additive white noise (AWN), nk, having zero mean and variance σn2, gives rise to the following received signal:rk=sk+nk.The matched filter (MF) is characterized by the following impulse response:hk=sT−k.The output of the MF, yk, accordingly, is given by the convolution of the impulse response and the received signal:yk=hk*rk=hk*(sk+nk),which, by the properties of convolution, is:yk=hk*sk+hk*nk.
The filter output, yk, therefore, is seen to be composed of a signal component—the convolution with the original signal, hk*sk—and a noise component—the convolution with the corrupting noise, hk*nk. It is known, moreover, that the filter output attains its maximum average value at the time instant, T, since there is a maximum correlation between the MF impulse response and template at the lag T. This, in turn ensures a maximum of the signal-to-noise (SNR) ratio at the output, which is defined as the ratio of the total energy of the signal template divided by the noise variance:
      S    ⁢                  ⁢    N    ⁢                  ⁢    R    =            1              σ        n        2              ⁢                  ∑                  k          =          0                T            ⁢                        s          k          2                .            
If the proper lag, T, for sampling the output of the matched filter is known, then this statistic based upon the output of the MF can be compared with a threshold in order to detect in a probabilistic sense the presence or absence of an original signal, sk.
Notwithstanding the advantages obtained with the matched filter, the underlying operations for processing signals with the filter tend not to adequately incorporate into a single functional measure both the time structure and the statistical distribution of time series or other sequential data corresponding to a signal sequence. Accordingly, there is a need for an enhanced matched filter that incorporates both signal aspects into a single functional measure.